Game Development Reference
In-Depth Information
Your target now becomes finding a way to eliminate the second column value
from the first row. To accomplish this, you multiply the second row by a number
that transforms it so that when you add it to the second row you eliminate the
target value. This number is
3
. To carry out these activities, you proceed in this
way:
0
1
2
The original row
:
4
3
8
3
Multiplied by
4
3
:
Given this transformation of the second row, you add it to the first:
0
4
3
1
3
1
First row
:
4
3
8
3
0
Transformed second row
:
9
3
1
0
The result of the addition
:
1
0
3
Simplify the first row
:
Your matrix now assumes its final form:
103
012
Given this matrix, you can identify the solutions of the system as
x ¼
3and
y ¼
2.
Exercise Set 11.7
Here are some systems of equations to transform into matrices and solve for two values.
a. 3x þ 2y ¼4
5x y ¼ 2
b. 5x þ 2y ¼ 7
6x þ y ¼ 8
c. 3x þ 2y ¼4
2x y ¼5
d. a þ 4b ¼ 8
3a þ 5b ¼ 3
e. 6a 2b ¼ 4
7a þ b ¼ 13
